I wonder how county clerks who are observant Christians have handled the licensing of the sale of alcoholic beverages. My cousin is county clerk (not in Kentucky) and that is one of her duties. I don’t think she has a religious compunction against the consumption of alcohol, but I know many who do.
Methinks you grossly overestimate how many Christians oppose alcohol consumption; correlation is practically nonexistent.
You also are using an analogy where the licensed activity has been normalized long before one accepts a job which includes that facilitation.
The problem in this case is that Davis became County Clerk _before_ the KY definition involved was changed by judges outside her jurisdiction. Yes she may choose to step down, but it is also reasonable to refuse to facilitate an activity which was not part of the job description, and address that refusal on religious grounds WITHOUT being incarcerated for a mere administrative paperwork dispute.
It’s the old “living near an airport” issue: moving to a home next to an airport and then complaining about the noise is one thing, moving to a home which an airport is built next to much later is quite different. Your cousin KNEW issuing alcohol-related licenses was part of the job before she signed up for it. Davis didn’t know she’d have to facilitate activity that a great many consider morally reprehensible (way more than oppose alcohol availability).